Part 5 - XY-Wings & XYZ Wings, by Dan LeKander

Part 5 - DAN’S STEP 4 FOR SOLVING SUDOKU PUZZLES

Recap in past issues:

• August 2015 – Introduction -  Part 1–Sudoku Puzzle Preparation for Dan’s steps 1-8
  
• September 2015 – Step 1 - Part 2–Sudoku Pairs, Triplets and Quads, by Dan LeKander
• October 2015 – Step 2 - Part 3–Turbos & Interaction, by Dan LeKander
• November 2015 – Step 3 - Part 4–Sudoku Gordonian Rectangles and Polygons, by Dan LeKander

STEP 4 … XY-WINGS & XYZ-WINGS

Keep the faith. The name sounds much more complex than the technique! These steps are actually a barrel of fun … easy to detect and very useful in eliminating options in unsolved cells.

XY-WINGS

Example 1

In Example 1 above,  boxes 1, 2, & 3, from a real puzzle, are shown. The yellow highlighted cells in box 1 and 3 form a triplet. We will term cell C9R1 (column 9, row 1) the Driver Cell, because it “relates” to both of the other yellow cells.

Here is the theory; C9R1 has options 8 and 9, so therefore C9R1 must be an 8 or 9. If the driver cell is an 8, then C3R1 = 6, because it’s in the same box/row. In this case the blue highlighted cells cannot be a 6, because they’re in the same box/row. If the driver cell is a 9, then C7R2 = 6, because it’s in the same box and therefore the blue highlighted cells cannot be a 6. So regardless whether the driver cell is an 8 or 9, the blue cells cannot be a 6, and therefore the 6 can be eliminated as an option for these three cells.

Detecting this technique … start with box 1 and look for two unsolved cells with just two options that share one number in common. Then look for a two digit unsolved cell that is in the same column or row, of one of the two starting cells, which completes the triplet. Determine the Driver Cell; apply the theory.

XYZ-WINGS

Example 2

Example 2 illustrates another triplet in two different boxes. You’ll note that the two yellow unsolved cells, in box 5, contain a 3 digit option and a 2 digit option, whereas they share two options in common. In box 8, cell C5R9 forms the missing link for a triplet. The key point here is that both cells C4R6 and C5R9 have two options in common with C5R5, but are not the same two options. We will label C5R5 the Driver Cell.

Here is the theory; if the Driver Cell is a 3, then the blue cells are not a 3, because they’re in the same column. If the Driver Cell is a 2, then C5R9 = 3 and the blue cells are not a 3, because they’re in the same column. If the Driver Cell is a 5, then C4R6 = 3 and the blue cells are not a 3, because they’re in the same box. So regardless of which number in the Driver Cell is the correct number, the blue cells cannot be a 3. Therefore you may eliminate the 3 as an option for the blue cells.

Detecting this technique … search each box, 1 through 9, for a situation where there exists a two digit cell and a three digit cell, where they share two options in common. Find the third cell in a different box, but in the same column or row as the Driver Cell (three digit cell), that share two digits in common with the Driver Cell and completes the triplet. The two cells that relate to the Driver Cell must not have the same two options.

For fun, can you also find an XY-Wing in Example 2?

By Dan LeKander, Wellesley Island, NY

Dan LeKander and his wife, Peggy, have been seasonal residents of Fineview, on Wellesley Island, since 1983.  In addition to being a Sudoku addict, Dan explores the 1000 Islands to enjoy the wildlife, beauty, and of course, Catch-and Release bass fishing.

[See Jessy Kahn’s Book Review, “3 Advanced Sudoku Techniques…” by Dan LeKander, June issue of TI Life.]